Chapter 7_Case Study
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Chapter 7: Case Problem 2. Consumer Research Inc.
Introduction
This report analyzes credit card usage data from 50 consumers, provided by Consumer Research,
Inc. Our goal is to identify consumer characteristics that predict annual credit card charges. We'll
use descriptive statistics to summarize the data and regression analysis to explore relationships between income, household size (independent variables) and annual charges (dependent variable). The analysis will identify which variable is a better predictor and culminate in a multiple regression model for improved prediction. Finally, we'll discuss the model's limitations and suggest additional variables for future research.
Descriptive Statistics: Data Summarization
This section analyzes the income, household size, and credit card spending patterns within the sample population. The findings provide valuable insights into the characteristics of this group and can inform future decision-making strategies.
Income Distribution
Mean Income: $43,480 represents the average income within the sample.
Range and Skewness: The data exhibits a wider range of income levels, indicating a diverse sample population. Furthermore, the right skewness suggests a higher concentration of individuals with lower incomes compared to those with higher incomes. Understanding this distribution can be crucial for tailoring marketing campaigns or product offerings to specific income brackets.
Household Size
Mean Household Size: The average household size in the sample is 3.42.
Range and Skewness: The data displays a narrower range for household size, suggesting relative stability in the number of individuals per household within the sample. This information can be helpful for understanding the consumption patterns and needs of typical households within the group.
Credit Card Spending Patterns
Mean Amount Charged: The average amount charged on credit cards within the sample is
$[3,964.06].
Range and Skewness: While spending patterns exhibit some variability, the distribution shows less skewness compared to income. This suggests a wider range of spending habits
but without a significant concentration at extreme. Analyzing spending patterns can inform strategies for promoting specific products or services, loyalty programs, and overall customer engagement.
The analysis reveals a sample population with varying income levels, relatively stable household sizes, and diverse credit card spending patterns. This information highlights the importance of considering these factors when developing marketing initiatives, product offerings, and customer
service strategies. By understanding the demographics and spending behaviors of the target audience, businesses can tailor their approach to maximize customer satisfaction and achieve long-term success.
Regression with Income:
The regression equation is: Annual credit card charges = 2,203.9996 + 40.4798 * Income ($1000)
R-Squared (R^2) = 0.3981
The coefficient for income is statistically significant (p-value < 0.05), indicating that income has a significant impact on credit card charges.
The Estimated Regression Equations Using Household Size as the Independent Variable
The regression equation is:
Annual Credit Card Charges = 2,581.941 + 404.128 *Household Size
R-squared (R^2) = 0.5668
The coefficient for household size is statistically significant (p-value < 0.05), indicating that household size is a significant predictor of credit card charges.
The R-squared value is higher for the regression with household size (0.5668) compared to the regression with income (0.3981). This indicates that household size explains a larger portion of the variance in credit card charges compared to income. Both income and household size have statistically significant coefficients, suggesting that both variables have a significant impact on credit card charges.
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